Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicu

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Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the n th orbital will therefore be proportional to :

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According to the question, ​ 2 π r = n λ = p nh ​ = mv nh ​ or mvr = 2 π nh ​ or mv = 2 π r nh ​ F = qv B ​ = r mv 2 ​ or, q B ​ = r mv ​ = 2 π r ⋅ r nh ​ or, r 2 = 2 π qB nh ​ or, r = 2 π qB nh ​ ​ i.e., r ∝ n 1/2 ​

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